Finding a point part way between two points | Analytic geometry | Geometry | Khan Academy

TL;DR

Find point B on segment AC such that the ratio of AB to BC is 3:1.

Transcript

Find the point B on segment AC, such that the ratio of AB to BC is 3 to 1. And I encourage you to pause this video and try this on your own. So let's think about what they're asking. So if that's point C-- I'm just going to redraw this line segment just to conceptualize what they're asking for. And that's point A. They're asking us to find some poi... Read More

Key Insights

• 🥳 The ratio of AB to BC is 3:1.
• 😥 Point B is located 1/4 of the way between points A and C.
• 🚥 The problem can be approached by calculating horizontal and vertical distances separately.
• 🫥 One can visually determine the position of point B on the line segment using the intersection method.
• 😥 The coordinates of point B are (-3, 2).
• 🔙 The distance CB is 1/3 the distance BA.
• ❓ The problem can be solved using the distance formula or the Pythagorean theorem.

Questions & Answers

Q: How can the problem of finding point B be approached?

The problem can be approached by breaking it down into horizontal and vertical changes between points A and C. We can calculate the horizontal and vertical distances separately to find B.

Q: What are the horizontal and vertical distances between points A and C?

The horizontal distance between A and C is 16 units, while the vertical distance is 4 units.

Q: How can we determine the coordinates of point B?

To find the coordinates of point B, we need to move 1/4 of the way from C to A both vertically and horizontally. This will result in the coordinates (-3, 2) for point B.

Q: How can we visually determine the position of point B on the line segment?

We can visually determine the position of point B by marking the 1/4 distance on either the horizontal or vertical axis and finding the intersection point on the line segment.

Summary & Key Takeaways

• The task is to find point B on segment AC, with a specific ratio of AB to BC.

• The distance between B and A is 3 times the distance between B and C.

• The problem can be solved by breaking it down into vertical and horizontal changes between point A and point C.